Energy Calibration of Nonlinear Microcalorimeters with Uncertainty Estimates from Gaussian Process Regression.

The nonlinear energy response of cryogenic microcalorimeters is usually corrected through an empirical calibration. X-ray or gamma-ray emission lines of known shape and energy anchor a smooth function that generalizes the calibration data and converts detector measurements to energies. We argue that this function should be an approximating spline. The theory of Gaussian process regression makes a case for this functional form. It also provides an important benefit previously absent from our calibration method: a quantitative uncertainty estimate for the calibrated energies, with lower uncertainty near the best-constrained calibration points.

Absolute energies and emission line shapes of the L x-ray transitions of lanthanide metals.

We use an array of transition-edge sensors, cryogenic microcalorimeters with 4 eV energy resolution, to measure L x-ray emission-line profiles of four elements of the lanthanide series: praseodymium, neodymium, terbium, and holmium. The spectrometer also surveys numerous x-ray standards in order to establish an absolute-energy calibration traceable to the international system of units for the energy range 4 keV to 10 keV. The new results include emission line profiles for 97 lines, each expressed as a sum of one or more Voigt functions; improved absolute energy uncertainty on 71 of these lines relative to existing reference data; a median uncertainty on the peak energy of 0.24 eV, four to ten times better than the median of prior work; and six lines that lack any measured values in existing reference tables. The 97 lines comprise nearly all of the most intense L lines from these elements under broad-band x-ray excitation. The work improves on previous measurements made with a similar cryogenic spectrometer by the use of sensors with better linearity in the absorbed energy and a gold x-ray absorbing layer that has a Gaussian energy-response function. It also employs a novel sample holder that enables rapid switching between science targets and calibration targets with excellent gain balancing. Most of the results for peak energy values shown here should be considered as replacements for the currently tabulated standard reference values, while the line shapes given here represent a significant expansion of the scope of available reference data.

A Robust Principal Component Analysis for Outlier Identification in Messy Microcalorimeter Data.

A principal component analysis (PCA) of clean microcalorimeter pulse records can be a first step beyond statistically optimal linear filtering of pulses toward a fully nonlinear analysis. For PCA to be practical on spectrometers with hundreds of sensors, an automated identification of clean pulses is required. Robust forms of PCA are the subject of active research in machine learning. We examine a version known as coherence pursuit that is simple and fast and well matched to the automatic identification of outlier records, as needed for microcalorimeter pulse analysis.

A practical superconducting-microcalorimeter X-ray spectrometer for beamline and laboratory science.

We describe a series of microcalorimeter X-ray spectrometers designed for a broad suite of measurement applications. The chief advantage of this type of spectrometer is that it can be orders of magnitude more efficient at collecting X-rays than more traditional high-resolution spectrometers that rely on wavelength-dispersive techniques. This advantage is most useful in applications that are traditionally photon-starved and/or involve radiation-sensitive samples. Each energy-dispersive spectrometer is built around an array of several hundred transition-edge sensors (TESs). TESs are superconducting thin films that are biased into their superconducting-to-normal-metal transitions. The spectrometers share a common readout architecture and many design elements, such as a compact, 65 mK detector package, 8-column time-division-multiplexed superconducting quantum-interference device readout, and a liquid-cryogen-free cryogenic system that is a two-stage adiabatic-demagnetization refrigerator backed by a pulse-tube cryocooler. We have adapted this flexible architecture to mate to a variety of sample chambers and measurement systems that encompass a range of observing geometries. There are two different types of TES pixels employed. The first, designed for X-ray energies below 10 keV, has a best demonstrated energy resolution of 2.1 eV (full-width-at-half-maximum or FWHM) at 5.9 keV. The second, designed for X-ray energies below 2 keV, has a best demonstrated resolution of 1.0 eV (FWHM) at 500 eV. Our team has now deployed seven of these X-ray spectrometers to a variety of light sources, accelerator facilities, and laboratory-scale experiments; these seven spectrometers have already performed measurements related to their applications. Another five of these spectrometers will come online in the near future. We have applied our TES spectrometers to the following measurement applications: synchrotron-based absorption and emission spectroscopy and energy-resolved scattering; accelerator-based spectroscopy of hadronic atoms and particle-induced-emission spectroscopy; laboratory-based time-resolved absorption and emission spectroscopy with a tabletop, broadband source; and laboratory-based metrology of X-ray-emission lines. Here, we discuss the design, construction, and operation of our TES spectrometers and show first-light measurements from the various systems. Finally, because X-ray-TES technology continues to mature, we discuss improvements to array size, energy resolution, and counting speed that we anticipate in our next generation of TES-X-ray spectrometers and beyond.

The Practice of Pulse Processing.

The analysis of data from x-ray microcalorimeters requires great care; their excellent intrinsic energy resolution cannot usually be achieved in practice without a statistically near-optimal pulse analysis and corrections for important systematic errors. We describe the essential parts of a pulse-analysis pipeline for data from x-ray microcalorimeters, including steps taken to reduce systematic gain variation and the unwelcome dependence of filtered pulse heights on the exact pulse-arrival time. We find these steps collectively to be essential tools for getting the best results from a microcalorimeter-based x-ray spectrometer.

Note: Operation of gamma-ray microcalorimeters at elevated count rates using filters with constraints.

Microcalorimeter sensors operated near 0.1 K can measure the energy of individual x- and gamma-ray photons with significantly more precision than conventional semiconductor technologies. Both microcalorimeter arrays and higher per pixel count rates are desirable to increase the total throughput of spectrometers based on these devices. The millisecond recovery time of gamma-ray microcalorimeters and the resulting pulse pileup are significant obstacles to high per pixel count rates. Here, we demonstrate operation of a microcalorimeter detector at elevated count rates by use of convolution filters designed to be orthogonal to the exponential tail of a preceding pulse. These filters allow operation at 50% higher count rates than conventional filters while largely preserving sensor energy resolution.

A high resolution gamma-ray spectrometer based on superconducting microcalorimeters.

Improvements in superconductor device fabrication, detector hybridization techniques, and superconducting quantum interference device readout have made square-centimeter-sized arrays of gamma-ray microcalorimeters, based on transition-edge sensors (TESs), possible. At these collecting areas, gamma microcalorimeters can utilize their unprecedented energy resolution to perform spectroscopy in a number of applications that are limited by closely-spaced spectral peaks, for example, the nondestructive analysis of nuclear materials. We have built a 256 pixel spectrometer with an average full-width-at-half-maximum energy resolution of 53 eV at 97 keV, a useable dynamic range above 400 keV, and a collecting area of 5 cm(2). We have demonstrated multiplexed readout of the full 256 pixel array with 236 of the pixels (91%) giving spectroscopic data. This is the largest multiplexed array of TES microcalorimeters to date. This paper will review the spectrometer, highlighting the instrument design, detector fabrication, readout, operation of the instrument, and data processing. Further, we describe the characterization and performance of the newest 256 pixel array.